A383459 Minimum number of cycles in any permutation in S_n of the highest order (A000793(n)).

1, 1, 1, 1, 2, 1, 2, 2, 2, 3, 2, 3, 4, 3, 3, 3, 4, 3, 4, 5, 5, 4, 4, 5, 4

Offset

1,5

Comments

Landau's function g(n) = A000793(n) gives the maximum order of any permutation on n elements.

The number of permutations of order g(n) is A074059, and the number of different cycle types of permutations of order g(n) is A074064. a(n) is the maximum number of cycles in any permutation of order g(n), and A383459(n) is the minimum number of cycles in any permutation of order g(n).

Links

Table of n, a(n) for n=1..25.

Example

There are two different cycle types of permutations in S_6 of the maximum order g(6) = 6, for example (123456) and (12)(345)(6). The minimum number of cycles is a(6) = 1 and maximum number is A383458(6) = 3.

Crossrefs

Cf. A000793, A074059, A074064, A383458.

Sequence in context: A008677 A036497 A211976 * A035460 A261679 A147657

Adjacent sequences: A383456 A383457 A383458 * A383460 A383461 A383462

Keyword

nonn,more

Author

Anand Jain, Mar 22 2025

Status

approved